Modeling and simulation of procoagulant circulating tumor cells in flow
We describe a mathematical/computational model for thrombin concentration gradients generated by procoagulant circulating tumor cells (CTCs) in flow. We examine how CTCs enhance blood coagulation as they diffuse tissue factor (TF)-dependent coagulation enzymes in a flow environment with vessel walls...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2012-09-01
|
| Series: | Frontiers in Oncology |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fonc.2012.00108/full |
| _version_ | 1811273907410305024 |
|---|---|
| author | Angela eLee Garth William Tormoen Eva eKanso Owen eMcCarty Paul Kenneth Newton |
| author_facet | Angela eLee Garth William Tormoen Eva eKanso Owen eMcCarty Paul Kenneth Newton |
| author_sort | Angela eLee |
| collection | DOAJ |
| description | We describe a mathematical/computational model for thrombin concentration gradients generated by procoagulant circulating tumor cells (CTCs) in flow. We examine how CTCs enhance blood coagulation as they diffuse tissue factor (TF)-dependent coagulation enzymes in a flow environment with vessel walls. Concentration fields of various enzymes, such as prothrombin and thrombin, diffuse to and from CTCs, respectively, as they propagate through the bloodstream. The diffusion-dependent generation of these enzymes sets up complex time-dependent concentration fields. The CTCs are modeled as diffusing point particles in an incompressible fluid, and we exploit exact analytical solutions based on three-dimensional Green’s functions for unbounded domains with one wall for high-resolution numerical simulations. Time-dependent gradient trackers are used to highlight that concentration fields build up (i) near boundaries (vessel walls), (ii) in regions surrounding the diffusing particles, and (iii) in complex time-dependent regions of the flow where fields associated with different particles overlap. Two flow conditions are modeled: no flow, and unidirectional constant flow. Our results indicate that the CTC-generated thrombin diffuses to and persists at the blood vessel wall, and that the spatial distribution of CTCs in flow determines local thrombin concentration. The magnitude of the diffusion gradient and local thrombin concentration is dependent upon bulk solution concentrations of coagulation factors within normal reported concentration ranges. Therefore, our model highlights the potential to determine patient-specific risks for CTC-induced hypercoagulability as a function of CTC number and individual patient concentration of coagulation factors. |
| first_indexed | 2024-04-12T23:09:27Z |
| format | Article |
| id | doaj.art-7c55e488f8694611922ebc6550acb4c8 |
| institution | Directory Open Access Journal |
| issn | 2234-943X |
| language | English |
| last_indexed | 2024-04-12T23:09:27Z |
| publishDate | 2012-09-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Oncology |
| spelling | doaj.art-7c55e488f8694611922ebc6550acb4c82022-12-22T03:12:51ZengFrontiers Media S.A.Frontiers in Oncology2234-943X2012-09-01210.3389/fonc.2012.0010831006Modeling and simulation of procoagulant circulating tumor cells in flowAngela eLee0Garth William Tormoen1Eva eKanso2Owen eMcCarty3Paul Kenneth Newton4University of Southern CaliforniaOregon Health & Science UniversityUniversity of Southern CaliforniaOregon Health & Science UniversityUniversity of Southern CaliforniaWe describe a mathematical/computational model for thrombin concentration gradients generated by procoagulant circulating tumor cells (CTCs) in flow. We examine how CTCs enhance blood coagulation as they diffuse tissue factor (TF)-dependent coagulation enzymes in a flow environment with vessel walls. Concentration fields of various enzymes, such as prothrombin and thrombin, diffuse to and from CTCs, respectively, as they propagate through the bloodstream. The diffusion-dependent generation of these enzymes sets up complex time-dependent concentration fields. The CTCs are modeled as diffusing point particles in an incompressible fluid, and we exploit exact analytical solutions based on three-dimensional Green’s functions for unbounded domains with one wall for high-resolution numerical simulations. Time-dependent gradient trackers are used to highlight that concentration fields build up (i) near boundaries (vessel walls), (ii) in regions surrounding the diffusing particles, and (iii) in complex time-dependent regions of the flow where fields associated with different particles overlap. Two flow conditions are modeled: no flow, and unidirectional constant flow. Our results indicate that the CTC-generated thrombin diffuses to and persists at the blood vessel wall, and that the spatial distribution of CTCs in flow determines local thrombin concentration. The magnitude of the diffusion gradient and local thrombin concentration is dependent upon bulk solution concentrations of coagulation factors within normal reported concentration ranges. Therefore, our model highlights the potential to determine patient-specific risks for CTC-induced hypercoagulability as a function of CTC number and individual patient concentration of coagulation factors.http://journal.frontiersin.org/Journal/10.3389/fonc.2012.00108/fullcirculating tumor cellsprocoagulant circulating tumor cellschemical gradient trackingtissue factor and coagulationprothrombin and thrombin fieldscirculating tumor cell induced hypercoagulation |
| spellingShingle | Angela eLee Garth William Tormoen Eva eKanso Owen eMcCarty Paul Kenneth Newton Modeling and simulation of procoagulant circulating tumor cells in flow Frontiers in Oncology circulating tumor cells procoagulant circulating tumor cells chemical gradient tracking tissue factor and coagulation prothrombin and thrombin fields circulating tumor cell induced hypercoagulation |
| title | Modeling and simulation of procoagulant circulating tumor cells in flow |
| title_full | Modeling and simulation of procoagulant circulating tumor cells in flow |
| title_fullStr | Modeling and simulation of procoagulant circulating tumor cells in flow |
| title_full_unstemmed | Modeling and simulation of procoagulant circulating tumor cells in flow |
| title_short | Modeling and simulation of procoagulant circulating tumor cells in flow |
| title_sort | modeling and simulation of procoagulant circulating tumor cells in flow |
| topic | circulating tumor cells procoagulant circulating tumor cells chemical gradient tracking tissue factor and coagulation prothrombin and thrombin fields circulating tumor cell induced hypercoagulation |
| url | http://journal.frontiersin.org/Journal/10.3389/fonc.2012.00108/full |
| work_keys_str_mv | AT angelaelee modelingandsimulationofprocoagulantcirculatingtumorcellsinflow AT garthwilliamtormoen modelingandsimulationofprocoagulantcirculatingtumorcellsinflow AT evaekanso modelingandsimulationofprocoagulantcirculatingtumorcellsinflow AT owenemccarty modelingandsimulationofprocoagulantcirculatingtumorcellsinflow AT paulkennethnewton modelingandsimulationofprocoagulantcirculatingtumorcellsinflow |